Recently, a novel resource-efficient technique for the reporting channel transmissions in cooperative spectrum sensing was proposed. In this technique, secondary users are allowed to simultaneously send their local decisions to the fusion center, saving time and frequency resources. Expressions for the probabilities of detection and false alarm for the unitary-gain AWGN reporting channels were derived, while simulation results were given for both the AWGN and Rayleigh fading channels. Here, we provide an expression that is applicable to AWGN channels with different real-valued gains and to time-varying real-valued gains. A simple suboptimum receiver is proposed for the general complex-valued fading and non-fading channels, with an improved performance in the low signal-to-noise ratio condition. Numerical results are shown for both the AWGN and Rayleigh fading reporting channels, demonstrating the accuracy of the derived expressions and the attractive performance of the proposed receiver.